Apparatus and method for measuring a property of a layer in a multilayered structure

ABSTRACT

An apparatus measures a property of a layer (such as the sheet resistance of a conductive layer or thermal conductivity of a dielectric layer that is located underneath the conductive layer) by performing the following method: (1) focusing the heating beam on the heated a region (also called &#34;heated region&#34;) of the conductive layer (2) modulating the power of the heating beam at a predetermined frequency that is selected to be sufficiently low to ensure that at least a majority (preferably all) of the generated heat transfers out of the heated region by diffusion, and (3) measuring the power of another beam that is (a) reflected by the heated region, and (b) modulated in phase with modulation of the heating beam. The measurement in act (3) can be used directly as a measure of the resistance (per unit length) of a conductive line formed by patterning the conductive layer. Acts (1)-(3) can be repeated during fabrication of a semiconductor wafer, at each of a number of regions on a conductive line, and any change in measurement indicates a corresponding change in resistance of the line. When the measurement changes by more than a predetermined amount (e.g. by 10%), a process parameter that controls the fabrication process is changed to return the measurement to normal in the next wafer. Moreover, the thermal conductivity of the dielectric layer can be measured, or monitored for changes beyond a predetermined limit during a scan across the wafer, if resistance is known.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to and incorporates by reference in theirentirety the following three commonly owned, copending U.S. patentapplications:

Ser. No. 08/638,944, entitled "SYSTEM AND METHOD FOR MEASURING THEDOPING CONCENTRATION AND DOPING PROFILE OF A REGION IN A SEMICONDUCTORSUBSTRATE", filed Apr. 24, 1996, by Peter G. Borden, now U.S. Pat. No.5,883,518.

Ser. No. 08/637,244, entitled "SYSTEM AND METHOD FOR MEASURINGPROPERTIES OF A SEMICONDUCTOR SUBSTRATE IN A FABRICATION LINE," filedApr. 24, 1996, by Peter G. Borden, now U.S. Pat. No. 5,966,019.

Ser. No. 09/095,804 entitled "AN APPARATUS AND METHOD FOR EVALUATING AWAFER OF SEMICONDUCTOR MATERIAL", filed Jun. 10, 1998, by Peter G.Borden et al.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the measurement of a property of alayer in a multilayered structure, and in particular to a measurement ofreflectance of a region of a conductive layer (such as a conductiveline), and use of the reflectance measurement to determine variousproperties, such as sheet resistance of the layer, and thermalconductivity of a dielectric layer located underneath the conductivelayer.

2. Description of Related Art

Metal lines having sub-micron (i.e. less than 1 micron) dimensions areconventionally used to interconnect devices that are formed in anintegrated circuit die. Such a metal line is typically formed as aportion of a film of metal (such as aluminum or copper). The metal filmis normally formed as a blanket layer over a semiconductor wafer, and isthereafter removed (e.g. by etching) to form one or more metal lines, ina process act known as "patterning". Conventionally, the resistivity ofthe metal film is measured (on a test wafer), and the measurement iscombined with a measurement of the film's thickness (on another testwafer) and, a measurement of the line width (on a production wafer), todetermine if the metal film has ohmic loss sufficiently low for use informing metal lines required in an integrated circuit die.

A number of methods exist for measuring a metal film's resistivity. Twosuch methods are commonly known as "probing" and "eddy current". In theprobing method, two or four probes are brought into physical contactwith an unpatterned metal film (e.g. on a test wafer) to measure thefilm's resistivity directly. See, for example, "The Four-Point Probe",Section 1.2, pages 2-20 in the book "Semiconductor Material and DeviceCharacterization" by Dieter K. Schroder, John Wiley & Sons, Inc, NewYork, 1990. In the eddy current method, a measurement device is coupledto the metal film either capacitively or inductively, i.e. withoutcontacting the metal film. See, for example, "Eddy Current", Section1.4.1, pages 27-30, in the book by Schroder (referenced above).

Each of the above-described methods requires a metallized region havinga width (e.g. 0.5 mm) that may be several orders of magnitude largerthan a typical metal line's width (e.g. <0.5 microns). Due to therequirement of the metallized region to have a 1000 times larger width,the measurements are performed prior to patterning, typically on a testwafer. Moreover, the above-described methods measure merely theresistivity of a metal film, and are not known to be used in themeasurement of resistance of a line formed after etching the metal film(e.g. in a production wafer).

U.S. Pat. No. 5,228,776 granted to Smith et al. (hereinafter "Smith")describes measuring changes in optical reflectivity (column 4, line 5-6)caused by thermal waves (column 3, line 42) to "monitor variations inelectrical conductivity and resistance . . . " (column 4, lines 53-54).Specifically, Smith requires "periodically exciting the sample at ahighly localized spot on the sample surface . . . The pump beamfunctions to periodically heat the sample which in turn generatesthermal waves that propagate from the irradiated spot . . . Features ator beneath the sample surface can be studied by monitoring thevariations they induce in these waves" (column 1, lines 25-40). Smithalso states that "when the optical reflectivity of the sample is to bemonitored, it is desirable to arrange the pump and probe beams to becoincident on the sample" (column 1, lines 60-64). When using suchcoincident beams, Smith notes problems created by "surfaces associatedwith defective vias are often not optically flat . . . " (column 3,lines 6-13). Moreover, prior art also states that "[w]hen materialsother than semiconductors are to be evaluated, such as metals . . .analysis of the thermal wave patterns is required" (see U.S. Pat. No.4,854,710 at column 7, lines 41-44).

SUMMARY OF THE INVENTION

According to the principles of the invention, an apparatus focuses abeam of electromagnetic radiation (also called "heating beam") on aregion (also called "heated region") of a conductive layer such thatheat generated by the beam transfers out of the heated region primarilyby diffusion, i.e. by conduction under steady state conditions, therebyeliminating the creation of a thermal wave as described in U.S. Pat. No.5,228,776.

Specifically, a method implemented by the apparatus (also called"measurement apparatus") includes (1) focusing the heating beam on theregion, (2) modulating the power of the heating beam at a frequency thatis predetermined to be sufficiently low to ensure that at least amajority (preferably almost all) of the generated heat transfers fromthe heated region by diffusion, and (3) measuring the power (also called"reflected power") of a portion of another beam (also called "probebeam"), the portion being (a) reflected by the heated region, and (b)modulated in phase with modulation of the heating beam.

In one embodiment, the above described acts (1)-(3) are repeated by themeasurement apparatus between various acts in the fabrication of asubstrate, at each of a number of regions on a line (formed bypatterning the conductive layer), and any change in the measurements ofthe reflected power indicates a corresponding change in resistance (perunit length) of a conductive line. In another embodiment, the conductivelayer is not patterned into a line, and instead the measurementapparatus performs the above-described acts on one or more regions of anunpatterned conductive layer, and measures the sheet resistance.

When the measurements change by more than a predetermined amount (e.g.by 10%), one embodiment of the measurement apparatus changes a processparameter that controls one of the fabrication acts (e.g. themetallization act) in a "feedback" loop to return the measurement tonormal in the next wafer (or next batch of wafers). Performance of acts(1)-(3) during a fabrication process, without touching a substrate (i.e.in a non-contact manner) increases yield of the fabrication process, ascompared to an off-line measurement of the resistivity of a metal filmon a test substrate. Also, performance of acts (1)-(3) as describedherein indicates the efficacy of patterning of the specific productionsubstrate that is otherwise not measurable e.g. when using anunpatterned substrate (such as a test substrate).

As noted above, the measurement apparatus modulates the power of theheating beam at a frequency (e.g. 1000 Hz) that is selected to besufficiently low to ensure that at least a majority (i.e. greater than50%) of the generated heat is transferred out of the heated region bydiffusion rather than by a thermal wave. The measurement apparatusdetects the reflected power that is also modulated at the just-describedfrequency, for example, by using a lock-in amplifier. Moreover, theapparatus filters, prior to the measurement, any portion of the heatingbeam that is also reflected, for example by using (a) a silicon wafer,or (b) a narrow band filter tuned to the wavelength of the probe beam,or preferably both, thereby eliminating the need for a quarter waveplate otherwise necessary in the prior art.

In one embodiment, the measurement apparatus includes sources (such aslasers) that produce each of the heating beam and the probe beam. Inaddition, the measurement apparatus also includes a photosensitiveelement (such as a "photodiode") that is located in the path of aportion of the probe beam reflected by the heated region. Thephotosensitive element generates an electrical signal (e.g. a voltagelevel) that indicates the intensity of the probe beam portion reflectedby the illuminated region. The intensity in turn indicates reflectancecaused by heating. So the intensity measurement is a measure of the peaktemperature in the heated region. In this embodiment the measurementapparatus also includes a computer that is coupled to the photosensitiveelement to receive the electrical signal, and that is programmed todetermine the value of a material property in the heated region from oneor more such measurements.

Use of diffusion as described herein to transfer a majority of thegenerated heat from the heated region is a critical aspect of theinvention, and eliminates the need for a thermal wave as describedabove. Transferring heat by diffusion as described herein causes aconductive line to have a steady-state temperature (called "peaktemperature") at the center of the heated region, and the peaktemperature changes in phase with modulation of the heating beam. As thereflectance of a conductive line varies linearly with the peaktemperature, the reflectance also changes in phase with modulation ofthe heating beam.

In a first embodiment, the measurement apparatus computes a ratio (alsocalled "steady-state ratio") of a change in reflected power to acorresponding change in the power of the heating beam, with the probebeam power constant, and uses the ratio as a measure of the resistanceof the conductive line. Specifically, the steady-state ratio whenmultiplied by a predetermined constant yields, per unit length, theresistance of the conductive line in the heated region. Therefore, theapparatus uses a change in the steady-state ratio as a measure of achange in the resistance of the conductive line between the heatedregions.

As shown below, the reflectance obtained by heating a conductive line asdescribed herein increases linearly with the power of the heating beam.The reflectance when plotted with respect to the power of the heatingbeam, yields a straight line. The slope of the straight line is thesteady state ratio. This slope is approximately a product of a number ofknown factors and the resistance per unit length of the conductive line.Therefore, the steady-state ratio provides a measure of the resistanceper unit length.

In a second embodiment, the measurement apparatus computes a ratio (alsocalled "steady-state ratio") of the reflected power to the power of theheating beam and uses the ratio as a measure of the resistance per unitlength of the conductive line. The second embodiment eliminates the needto perform at least two measurements that are otherwise required todetermine a straight line, and is based on the fact that the reflectedpower is zero when the power of the heating beam is zero (i.e. usesorigin as one of the points on the straight line described above). Notethat in one implementation, a steady state ratio is not computed, andinstead a measurement of the difference in reflected powers in thepresence and absence of a heating beam is used directly as a measure ofthe resistance of a line, e.g. when using a heating beam having unitpower.

Determination of a steady-state ratio (as described above) during thefabrication of a substrate (e.g. immediately after patterning) providesan accurate indication of a change in resistance of a conductive lineacross the various regions of the wafer. Specifically, monitoring thesteady-state ratio identifies an increase in a conductive line'sresistance e.g. due to voids or due to impurities segregated at grainboundaries both of which cannot be detected by visual inspectionmethods. Moreover, use of a steady-state ratio as a measure of aconductive line's resistance detects not only variations in resistivity,but also variations in thickness and in width of the conductive line.

Also, a difference in reflectance measurements as described hereinidentifies a change in a property of a material other than the materialof the conductive line. For example, a change in adhesion between aconductive line and an underlying insulation layer causes acorresponding change in the dissipation of heat from the conductive linethrough the underlying layer, and is detected as a change in thereflectance measurement. Moreover, such a difference in reflectancemeasurement also indicates a change in thermal conductivity of theunderlying layer, e.g. due to a change in porosity or density of thelayer. Specifically, the lower the thermal conductivity of theinsulation layer, the higher the temperature of the conductive line(assuming the average power of the heating beam stays the same).

Such a change in thermal conductivity also indicates a correspondingchange in the dielectric constant of the underlying material. Also, achange in the dielectric constant can indicate a change in thecapacitance between the conductive line and one or more adjacentconductors or the ground plane. The change in capacitance in turnindicates a change in the speed of transmission of signals in theintegrated circuit.

Note that the substrate that supports a conductive layer or a conductiveline can be any of the following: a silicon wafer that is processed toform integrated circuit dice, a glass plate that is processed to form aliquid crystal display or a resin (such as BT) core that is processed toform a printed circuit board.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates, in a block diagram, use of one embodiment of ameasurement apparatus of this invention with a metal formation apparatusfor forming a conductive layer and a metal etching apparatus forpatterning the conductive layer.

FIG. 1B illustrates, in the apparatus of FIG. 1A, a heating beam focusedon a region 111R of a conductive line 111 under steady state conditionswhile a probe beam is used to measure reflectance of region 111R.

FIG. 1C illustrates, in a graph, the temperature of heated region 111Rand of adjacent regions 111S and 111T in the conductive line of FIG. 1B.

FIG. 2 illustrates, in a flow diagram, a method for using the two beamsof FIG. 1B to measure a change in resistance of conductive line 111, anduse of the measurement to control the processing of wafers by the metalformation apparatus and metal etching apparatus in FIG. 1A.

FIG. 3 illustrates, in a block diagram, a measurement apparatus thatperforms the method illustrated in FIG. 2.

FIG. 4A illustrates the transfer of heat through a portion 111X (ofregion 111T in FIGS. 1B and 1C) and into dielectric layer 112 bydiffusion under steady state conditions.

FIG. 4B illustrates, in a cross-sectional view, a via 114 that couplesconductive line 111 of the type illustrated in FIG. 4A to anotherconductive line 113, and the transfer of heat from line 111 byconduction through the via.

FIG. 5 illustrates, in a graph, the rise (above ambient) of temperaturein ° C. of conductive line 111 (FIG. 4A) as a function of power levels(of 5, 2 and 1 mW for respective lines 501-503) of a heating beam thatilluminates region 111R of FIG. 1B.

FIG. 6 illustrates, in a graph, a change in reflectance (plotted along yaxis after scaling by a factor of 1000) of conductive line 111 (FIG. 4A)as a function of the powers of a heating beam as described above inreference to FIG. 5 for various thicknesses (of 0.2, 0.5 and 1.0 μm forlines 601-603 respectively) of conductive line 111 (having a width of0.25 μm).

FIG. 7 illustrates, in a graph, a signal generated by the amplifier ofFIG. 3 for multiple lines 111 having different resistances, when alllines 111 have the same reflectance (i.e. are formed of the samematerial).

FIG. 8A illustrates, in a graph, the change in reflectance (plottedalong y axis and multiplied by 10,000) as a function of the thickness ofan aluminum blanket film, with each of lines 801-804 being for adifferent level of degradation in resistivity.

FIG. 8B illustrates, in a graph, the change in reflectance (plottedalong y axis and multiplied by 10,000) as a function of the sheetresistivity (in ohms per square) of an aluminum blanket film for nodegradation in resistivity.

FIG. 9 illustrates, in a graph, an intensity measurement (plotted alongy axis in units of millivolts) as a function of length of a side of asquare region, for measurements taken at the centers of squares of analuminum layer 0.2 μm thick formed on 1 μm thick silicon dioxide layerthat in turn is deposited on a silicon substrate.

DETAILED DESCRIPTION

A processing unit 10 (FIG. 1A) can be operated in accordance with theinvention to create integrated circuit (abbreviated as "IC") dice byprocessing a substrate 104 to form a patterned substrate 105, measuringthe resistance of one or more conductive lines in patterned substrate105, and adjusting the processing in real time if necessary.Specifically, unit 10 includes a metal deposition apparatus 11 thatforms on substrate 104 a layer of conductive material (such as a metal)to form a metallized wafer 103 that is in turn processed by metaletching apparatus 12 that etches the film to form one or more conductivelines in substrate 105. Unit 10 also includes a resistance measurementapparatus 13 that measures the resistance of one or more of theconductive lines (e.g. line 111 in FIG. 1B) on patterned substrate 105,or of one or more regions on unpatterned substrate 103 or both (i.e.before and after patterning of the same substrate).

If the resistance measurement falls outside of the specifications for asubstrate 103 or 104, a process parameter can be adjusted by resistancemeasurement apparatus 13. One embodiment of apparatus 13 includes anoptional programmed computer 13C that drives an active signal on line 14that is coupled to metal etching apparatus 12, or on line 15 that iscoupled to metal formation apparatus 11, or both, depending on themeasurement. A change in the process parameter can be determinedautomatically by software in programmed computer 13C, or can be enteredby a human operator.

In one embodiment, an unpatterned substrate 103 is transferred toresistance measurement apparatus 13 for measurement of a property of aconductive layer formed thereon. Examples of such a property areconductivity and thickness as described below in reference to FIGS. 8A,8B and 9. Such an intermediate measurement provides a more immediatefeedback to control the operation of metal formation apparatus 11 ascompared to an otherwise long delay (several hours or days) betweenforming a conductive layer and etching a pattern.

Resistance measurement apparatus 13 determines, between acts offabricating unpatterned substrate 104 or patterned substrate 105 (FIG.1B), a measure of the electrical resistance by use of two coincidentbeams 101 and 102 of electromagnetic radiation (such as laser beams). Afirst beam (also called "heating beam") 101 has a power (also called"heating power") that is modulated at a predetermined frequency. Asecond beam (also called "probe beam") 102 is continuous, and is weakerthan first beam 101. First beam 101 is incident on and heats a region111R on substrate 104 or 105 to a temperature T, and second beam 102 isreflected by region 111R in phase with modulation of first beam 101,because temperature T is modulated in phase with modulation of firstbeam 101.

The predetermined frequency of modulation of first beam 101 is selectedto be sufficiently small to ensure that a majority (i.e. greater than50%) of heat generated by first beam 101 flows by diffusion out ofheated region 111R (e.g. along the length L of line 111 on substrate105). In one embodiment, the predetermined frequency is selected tocause substantially all (e.g. greater than 90%) of heat generated byfirst beam 101 in region 111R to be transferred to adjacent regions 111Sand 111T by diffusion. Such a diffusive heat transfer allows the use ofa diffusion equation solution (20) as described below to relateelectrical and thermal conductivity in a measurement method 200 (FIG.2). Therefore, the predetermined frequency is selected to be lower thana maximum frequency beyond which the effects of a thermal wave becomenoticeable. The maximum frequency is inversely related to a dimension ofheated region 111R (e.g. the length L) as described below in referenceto equation (11). In one embodiment, length L is approximately 100microns, and the maximum frequency is 1430 Hz for copper lines, and 1080Hz for aluminum lines.

Note that the following discussion makes a specific reference to aconductive line 111, although as noted later (in reference to FIGS. 8A,8B and 9) a similar analysis in applicable to a portion of a conductivelayer. Moreover, although the following description refers to a wafer ofsilicon (such as wafer 103, 104, or 105), the description is equallyapplicable to any substrate that supports a conductive layer, and otherexamples of such a substrate include a glass plate and a resin core. Forconvenience, the same reference numerals are used for a wafer and asubstrate.

The diffusion of heat from region 111R creates a temperature profile 150(FIG. 1C) in conductive line 111, with a hottest point C (having a peaktemperature T_(p)) located at the center of region 111R under thefollowing assumption. In one example, conductive line 111 is supportedon a dielectric layer 112 (FIG. 1B) of a wafer 105 having a thermalconductivity K_(i) that is almost two orders of magnitude lower than thethermal conductivity K_(m) of conductive line 111. Note that such alarge difference in thermal conductivities is not required for therelation in equation (20) described below. Instead, equation (20) holdsas long as the thermal conductivity K_(i) of dielectric layer 112 issmaller than the thermal conductivity Km of line 111.

Peak temperature T_(p) (FIG. 1C) is a function of the thermalconductivity K_(m) and the cross-sectional area Wh_(m) of conductiveline 111, wherein W is width and h_(m) is height of line 111. As theelectrical and thermal conductivities are related (as shown in equation(1)), peak temperature T_(p) indicates (as discussed more completelybelow), per unit length, conductive line 111's electrical resistance.

Temperature profile 150 has substantially the same "bell" shape (FIG.1B) over length L at any time during a cycle at the predeterminedfrequency. Therefore, temperature T is modulated without forming a wavein space (in a manner analogous to direct current ("DC")) during thecycle. Temperature T is modulated only to increase the accuracy inmeasurement, specifically the signal-to-noise ratio (described below inreference to equation 21) by use of synchronous detection of a portionof probe beam 102 reflected by region 111R. Moreover, the predeterminedfrequency can be arbitrarily low, limited only by the minimum throughputrequired of the fabrication process.

In one embodiment, a measure of the electrical resistance of line 111 isdetermined by performing acts 201-206 of a method 200 (FIG. 2).Specifically, in act 202, heating beam 101 is focused on a region 111R(FIG. 1B). In act 201 (FIG. 2), the power of heating beam 101 ismodulated at the predetermined frequency. Note that acts 201 and 202 canbe performed in reverse order, i.e. act 202 performed first followed byperformance of act 201.

Next, the power (also called "reflected power") of probe beam 102 afterreflection by region 111R is measured in act 203. Thereafter, in act204, the power of heating beam 101 (FIG. 1B) is changed, e.g. increasedfrom 1 milliwatt to 5 milliwatts. Next, in act 205 (FIG. 2), a change inthe reflected power in response to the change in power of heating beam101 is determined. Thereafter, in act 206, a ratio of the change inreflected power to the change in power of heating beam 101 is computed.The ratio indicates, per unit length, a measure of the electricalresistance of conductive line 111 in region 111R. Note that during thejust-described operations, the power (also called "probe power") ofprobe beam 102 that is incident on region 111R remains constant in thisembodiment. The ratio may itself be compared (in act 207) with apredetermined limit to check if line 111 is within specifications and ifso, return to act 201 (for another wafer).

The ratio (also called "steady-state ratio"), when multiplied by apredetermined constant yields, per unit length, the resistance ofconductive line 111 in heated region 111R. As described more completelybelow, the constant's value is determined (see equation (20)) by anumber of factors, such as absolute reflectance R_(o) of the conductiveline 111 in heated region 111R, dielectric constant of free space ε₀,frequency of modulation ν_(L) of the reflected portion of probe beam102, Boltzmann's constant k_(B), electron charge q, ambient temperatureT_(o), rate of change of resistivity with temperature, and power ofprobe beam 102, as well as the thickness h_(i) and thermal conductivityK_(i) of insulating layer located underneath the conductive line. Thesteady-state ratio when multiplied by such a constant yields (ρ_(e)/Wh_(m)) where ρ_(e) is the resistivity, W is the width of conductiveline 111 and h_(m) is the thickness of conductive line 111.

In one implementation, heating beam 101 is focused (in act 210) inanother region (e.g. region 111T) and the measurement is repeated (inact 203), and the two measurements are compared. Any reduction in widthW or height h_(m) results in an increase in the steady-state ratio thatcan be detected by the comparison. Similarly, any increase inresistivity also increases the steady-state ratio, and is also detectedby the just-described comparison. Furthermore, a problem in adhesion ofconductive line 111 to the underlying dielectric layer 112 (e.g. due tovoids or delamination) also causes an increase in the steady-state ratioand is therefore also detected by the comparison.

In one implementation, the above-described measurements (either a singlemeasurement or two or more measurements per region) are repeated afterfocusing (see act 210) heating beam 101 in each of three differentregions that define a triangular area on conducive line 111. Instead ofcomparing numerical measurements, a change in the steady state ratio canbe detected by plotting a graph of the steady state ratio as a functionof distance.

Therefore, the event of a change in the steady-state ratio (e.g.exceeding a predetermined limit) provides an indication that thefabrication process has changed, and that conductive line 111 is nolonger within the specification. In response to the indication, anoperator or an appropriately programmed computer changes a processparameter that controls the fabrication of line 111 (see act 208 in FIG.2) and that changes the process to return a conductive line in the nextwafer to within the specification. For example, the operator identifiesa source of contamination in metal formation apparatus 11 (FIG. 1A) thatdegrades the resistivity of a metal layer formed on wafer 103, andchanges a parameter related to the source.

A steady-state ratio as described above is measured at a single spot(e.g. in region 111R), allowing the measurement (of the value ofreflected power) to be made in a more compact area (e.g. a region oflength 1 micron) than possible by a method that requires two locations(each displaced from the other), e.g. as disclosed in U.S. Pat. No.5,228,776. In the just-described example, since only the power of beam101 that is incident on line 111 heats the line, width W (FIG. 1B) ofline 111 can be smaller than the diameter of beam 101 (that may have aminimum size larger than line width W). The temperature of a region 111R(of length equal to the diameter of beam 101) in line 111 that is heatedunder diffusive conditions as described herein is a function of thethermal properties of an extended length L (typically several tens ofmicrons) of line 111 about the heated region 111R.

In the prior art (e.g. U.S. Pat. No. 5,228,776), the heat propagatesaway from a heated region in a thermal wave, and the temperature at theheated region is not a direct function of the physical properties of theconductive line at a distance. This is because a thermal wave at anypoint is the sum of heat from an outgoing wave and heat from wavesreflected from one or more regions in the line where the metalproperties have changed. This sum is difficult to quantify in the priorart, because the reflective properties of defects may not be known inadvance.

In contrast, during diffusive heat transfer, the heat at any point isaffected in a quantifiable manner (as described below in reference toFIG. 4B) by the reflective properties of defects or vias at a distancefrom the point. Also, method 200 provides an unexpected result,specifically the value of reflected power as measured by method 200 isunaffected by the presence of non-flat surfaces (that cause problems inthe prior art, e.g. U.S. Pat. No. 5,228,776) because a reflectancemeasurement as described herein is independent of the small angulardeflection that is caused by periodic undulation of a surface by passageof a thermal wave.

In one example, apparatus 13 operates heating beam 101 at 0.001 wattsand at 0.002 watts and obtains intensity measurements for these twopower as follows: probe beam has an incident power on heated region 111Rof 1.1 milliwatts, and (1) a modulated component of reflected power of0.55 microwatts, thereby yielding ΔR=(0.55/1.1)×10⁻³ =0.5×10⁻³ ; and (2)a modulated component of the reflected power of 1.1 microwatts, therebyyielding ΔR=(1.1/1.1)×10⁻³ =1×10⁻³. Therefore, the slope isΔR/ΔP=(1.0-0.5)/(0.002-0.001)×10⁻³ =0.5. The value of 0.5 of the slopeis thereafter used with a constant (as described below in reference toequation 20) to obtain the resistance per unit length. Note that insteadof using two measurements, a single measurement (e.g. at 0.001 watts ofheating beam power) can be used, e.g. by computing ΔR/ΔP as(0.5/0.001)×10⁻³ =0.5 assuming that the ΔR is zero when ΔP is zero.

In an alternative embodiment, instead of performing acts 204-206,another ratio is computed in act 209, directly after act 203, based onthe fact that a modulated component of the reflected power is zero whenthe power heating beam 101 is zero. Specifically, a ratio of a modulatedcomponent of the reflected power to the power of heating beam 101 iscomputed, and used as a measure, per unit length, of the electricalresistance of conductive line 111 in act 207. Furthermore, instead ofcomputing the ratio, the reflected power can also be used directly (bygoing from act 203 directly to act 207 or by going from act 205 directlyto act 207) as a measure of the electrical resistance per unit length,if power of heating beam 101 is constant for each of a number ofmeasurements for the corresponding regions e.g. regions 111R-111T.

Use of steady-state conditions as described herein eliminates the needfor a generation beam having the high modulation frequency required byU.S. Pat. No. 5,228,776 to set up a thermal wave. Specifically, theabove-described method eliminates the need to generate a beam modulatedat a frequency in the range of 1 MHz to 100 MHz, and instead requires abeam modulated at a frequency that is several orders of magnitudesmaller, e.g. in the range of 0.01 KHz to 1 KHz, thereby eliminating thethermal wave.

Acts 201-206 of method 200 can be performed by use of a resistancemeasurement apparatus 13 (FIG. 3) having two lasers that create the twobeams 101 and 102. Specifically, apparatus 13 includes a laser 301 forcreating a beam 101 of electromagnetic radiation at a predeterminedwavelength, such as infrared light, ultraviolet light, X-rays, gammarays, or radiation in the microwave or radio frequencies. In a preferredembodiment, laser 301 is a AlGaAs diode laser that emits electromagneticradiation of wavelength 830 nm.

The electromagnetic radiation created by laser 301 is transmittedthrough an optical fiber 302 to a collimator 323 that emits heating beam101. In one implementation, heating beam 101 has a maximum power of, forexample, 100 milliwatts. Apparatus 13 also includes lenses 304A and 304Bthat adjust the size of beam 101 to fill the aperture of an objectivelens 315 also included in apparatus 13.

Apparatus 13 further includes a second laser 305 that creates a beam 102of electromagnetic radiation used to measure a change in reflectance ofregion 111R (FIG. 1B) in response to change in power of heating beam101. In one implementation, laser 305 is an InGaAs diode laser thatemits electromagnetic radiation of wavelength 1480 nm. Theelectromagnetic radiation created by laser 305 is transferred by anoptical fiber 306 to another collimator 307 also included in apparatus13. Collimator 307 emits probe beam 102 having a maximum power of, forexample, 7 milliwatts. Therefore, probe beam 102 has a power that is anorder of magnitude smaller than the power of heating beam 101, so thatconductive line 111 is not noticeably heated by probe beam 102.

Apparatus 13 also includes lenses 308A and 308B that adjust the size ofprobe beam 102 to fill the aperture of objective lens 315 (describedabove). Apparatus 13 also includes a dichroic beam splitter 310 thatcombines heating beam 101 and probe beam 102 to form a combined beam311. Combined beam 311 passes through beam splitters 312 and 314 thatare also included in apparatus 13, to an objective lens 315. Objectivelens 315 can be, for example, a 0.9 NA, 100× objective lens availablefrom Nikon of Yokohama, Japan. A portion of combined beam 311 isdeflected to a photodetector 313, such as part number J16-8SP-RO5m-HSfrom EG&G Judson of Montgomeryville, Pa., USA. Photodetector 313 is usedto verify the alignment of combined beam 311 with respect to wafer 105,and to measure the incident power of one or both of beams 101 and 102.

Light reflected from wafer 105 passes back through objective lens 315and through beam splitter 312. Beam splitter 312 sends 50% of thereflected light through a filter 319 to a photodetector 320. Filter 319is a narrow band filter that removes the reflected portion of heatingbeam 303 while passing the reflected portion of probe beam 309.Thereafter, photodetector 320 senses the intensity of the reflectedportion of probe beam 309, and passes a voltage signal to amplifier 324.

Amplifier 324 converts the voltage signal into a current signal andpasses the current signal to a lock-in amplifier 322. Lock-in amplifier322 includes an oscillator as a frequency source that is used to detectthe power of the reflected portion of probe beam 102 modulated at thepredetermined frequency. The frequency source in lock-in amplifier 322also provides a frequency signal on a line 321M to a laser driver 321.Laser driver 321 uses the frequency signal on line 321M to drive laser301 at the predetermined frequency that is sufficiently low to modulatethe amplitude of heating beam 303 to ensure heat transfer by diffusionas described herein.

Apparatus 13 also includes a beam splitter 314 that diverts 10% ofcombined beam 311 to a focusing lens 317 and a camera 318. Camera 318 isused to observe beams 101 and 102 (FIG. 1B) on wafer 105, in order tofocus combined beam 311 (FIG. 3) within region 111R (FIG. 1B) on wafer.

The above-described method 200 uses one or more of the followingrelationships (under steady-state conditions) between conductive line111's thermal conductivity, electrical resistance, and reflectance toprovide a non-destructive yet reliable method for detecting changes inthe resistance of line 111. Specifically, the electrical resistance ofconductive line 111 (FIG. 4A) is determined using the Wiedermann-Franzequation ##EQU1## where Km is the thermal conductivity of line 111 inunits of watts/(cm-deg C.), σe is the electrical conductivity of line111 in units of (ohm-cm)⁻¹, T is the absolute temperature of line 111, qis the electron charge, and k_(B) is Boltzmann's constant.

The electrical resistivity of line 111 is the inverse of the electricalconductivity, ρ_(e) =1/σ_(e), in units of ohm-cm. The electricalresistance of line 111 is found by multiplying the electricalresistivity ρ_(e) by L/A, where A is the cross-sectional area Wh_(m)Wh_(m) (FIG. 1B) in units of centimeters squared and L is the length ofconductive line 111 in centimeters.

The electrical resistivity of conductive line 111 is related to thereflectance R of line 111 (a ratio of reflected power to the incomingpower) by the Hagen-Rubens relation: ##EQU2## where ν_(L) is thefrequency (in units of cycles per second) of the reflected portion ofprobe beam 102 (equal to c/λ, where c is the speed of light, 3×10¹⁰cm/sec, and λ is the wavelength of probe beam 102). Although the aboveequation (2) does not strictly hold at near-infrared wavelengths (e.g.wavelengths in the 0.75 to 2 μm range, corresponding to frequencies 1.5to 4×10¹⁴ Hz) for good conductors such as aluminum and copper, theimaginary part of the index of refraction greatly exceeds (e.g. by anorder of magnitude) the real, and the approximations used to deriveequation (2) hold approximately.

Hence, conductive line 111's reflectance R is directly related toelectrical resistivity ρ_(e) and thermal conductivity K_(m) by equations(1) and (2). Therefore, use of a heating beam 101 introduces a knownheat flux Q into line 111, thereby to heat line 111 to a peaktemperature T_(p) that is determined by measuring the reflectance R ofprobe beam 102. Line 111's electrical resistivity ρ_(e) is then deduceddirectly from equation (2).

Alternatively, as discussed below a solution of a heat-flow equation (3)yields line 111's thermal conductance per unit length as a function oftemperature T, thereby yielding line 111's electrical conductance perunit length and its inverse, the electrical resistance per unit length.The analysis provided below uses the following assumptions. Heat fluxH_(out) (x) flowing into a region of width Δx around a point 111X (FIG.4A) outside of region 111R (FIG. 1B) in line 111 is diffusive and hencetemperature profile 150 (FIG. 1C) has a static solution rather thanwave-like solution. Conductive line 111 (FIG. 1B) is a conductor thathas a length L assumed to be infinite along the X axis (as compared tothe diameter of heated region 111R). Moreover, conductive line 111 hasthermal conductivity K_(m), and lies on an insulation layer 112 with athermal conductivity K_(i) and thickness h_(i). The light from heatingbeam 101 that is not reflected is fully absorbed by line 111, creating aheat flux H (FIG. 1B) flowing in both the positive and negative Xdirections from heated region 111R.

Initially assume that heat flow F(x) into insulation layer 112 is smallcompared to flow H(x) along line 111--an assumption that is valid whenthe thermal conductivity of line 111 is much greater than the thermalconductivity of layer 112. The temperature T at any point 111X (FIG. 1C)along conductive line 111 is found by solving the one-dimension heatdiffusion equation for the difference in temperature T between line 111and the ambient: ##EQU3## The first term in equation (3) represents thediffusion of heat, which creates a static distribution. The second termrepresents the time-variation of the temperature, giving rise to thewave-like solution. The units of K_(m) are watts/(cm-deg. C.). Thethermal diffusivity K_(m) is related to the thermal conductivity K_(m)as κ_(m) =K_(m) /ρ_(m) C_(m), where ρ_(m) is the density of line 111 (inunits of gms/centimeter³) and C_(m) is the heat capacity (in units ofJoule/gm-degree C.) of line 111

Equation (3) is solved by separation of variables. Assume atime-dependent solution for temperature T of line 111 of the form

    ΔT(x,t)=u(x)e.sup.jωt                          (4)

where ω is the modulation frequency. Substituting (4) into (3) gives anequation in x, ##EQU4## The solution that is finite at infinity is##EQU5## Combining (4) and (6), the temperature as a function ofposition and time is

    ΔT(x,t)=Ae.sup.-kx cos(ωt-kx)                  (7)

where ##EQU6## A is a constant determined by the initial conditions, andω is radial frequency of the thermal wave.

Equation (7) is a wave solution, with a frequency f=ω/2π and awavelength λ given by equation (8). If the wavelength λ of the thermalwave is long compared to the dimensions of the measurement, then k inequation (8) will be small. If k is sufficiently small, the second termin equation (5)--representing the time dependence--will beinsignificantly small (e.g. less than 1%) compared to the staticderivative term. The assumption that k is small reduces equation (5) to##EQU7## Equation (9) has no time dependence, and is a steady stateequation for transfer of heat by diffusion, identical to equation (3)when d(ΔT)/dt=0 (with insignificant variation of ΔT with respect totime).

Assume L (FIG. 1B) is the length of line 111 over which heat diffuses toset up the steady state temperature distribution upon which themeasurement is based. The condition for a steady state solution is thatmeasurement length L must be negligibly small compared to the thermalwavelength: ##EQU8##

Using a factor of 10 (i.e. one order of magnitude) to signify "very muchgreater than", the equation for the modulation frequency is ##EQU9## Thetable below gives the relevant constants and the thermal wavelength λ at1000 Hz for various materials.

    ______________________________________                                               ρ     C      K        κ                                                                             @1 KHz                                 Material                                                                                g/cm3    J/g-K                                                                               W/cm-K   cm.sup.2 /sec                                                                       μm                                 ______________________________________                                        Aluminum                                                                             2.70      0.90   2.37     0.98  1105                                   Copper       8.96                                                                                0.39   3.98      1.14                                                                                        1197                        Tungsten                                                                                19.3      0.14                                                                                1.79      0.66                                                                                          911                       Silicon                                                                                   2.328                                                                               0.70    1.45      0.89                                                                                        1058                        ______________________________________                                    

For the above values and length of measurement L of 100 microns, thesteady-state approximation requires a modulation frequency of less thana maximum frequency of, e.g. 1430 Hz for copper and 1080 Hz foraluminum.

The maximum frequency is also inversely related to the distance overwhich the temperature T decays to, e.g. 10% of the peak temperatureT_(p). If such a distance (also called "decay distance") is smaller thanmeasurement length L, the maximum frequency can be higher than thejust-described maximum frequency. For example, if the decay distance is20 microns, the maximum frequency is 5985 hz for copper and 5525 hz foraluminum.

Temperature profile 150 (FIG. 1C) is determined by solving the staticheat equation for region 111R (FIG. 1B), taking into account heat lossinto insulation layer 112. Assume a region (not labeled) around point111X (FIG. 4A) of conductive line 111 has a length Δx, a width w, and athickness h_(m). Insulation layer 112 has thickness h_(i) and thermalconductivity K_(i), and is assumed to be at the temperature ofconductive line 111 at top surface 112T, and at the ambient temperatureat the bottom surface 112B.

Heat flux H(x) is primarily along conductive line 111, but a smallamount of heat F(x) leaks through insulation layer 112. By conservationof energy, H(x)=F(x)+H(x+dx), assuming negligible loss (less than 1%) toconvection and radiation. Such losses may be included as additionalterms added to the loss F(x) due to heat flow into insulator 112,(especially for convection, which scales as the temperature differencebetween the ambient and the insulator, as does the loss into theinsulator). The diffusive heat flux is given by the derivative of thetemperature times the thermal conductivity. Across the thickness h_(i)of insulation layer 112 the derivative is approximately T(x)/h_(i),giving ##EQU10## in the limit as dx approaches zero, equation (12)reduces to the equation for the temperature distribution in the metalunder the condition of diffusive heat flow, ##EQU11##

Solving equation (13) subject to the boundary conditions of ambienttemperature at infinity and an incident flux (1-R)P_(L) /2, where P_(L)is the heating laser power, R is the metal reflectance, and the factorof 2 arises because heat flows in both the +x and -x directions, givesthe temperature distribution as a function of the laser power andmaterial constants, ##EQU12## The thermal conductivity of insulationlayer 112 is typically about 1% of conductive line 111. For insulationlayer 112 having a thickness h_(i) of 1 μm, and a metal layer of equalthickness, the temperature drops to 1/e in about 10 microns. This iswell under the condition of 100 microns line length assumed above. Forexample, a laser power of 0.005 W on a 0.25 μm×0.5 μm when shone on analuminum line, with a reflectance of 90%, yields a temperature rise of35 degrees C.

Lines 501-503 (FIG. 5) illustrate the temperature rise for variouspowers (also called "reflected power") reflected by line 111 (FIG. 1A)in one exemplary wafer 105. In the examples of FIG. 5, line 111 has awidth w of 0.25 μm, and a thickness h_(m) of 0.5 μm, and is formed ofaluminum on a dielectric layer 112 formed of silicon dioxide and havinga thickness hi of 1 μm. For the following analysis, conductive line 111is assumed to be on an insulation layer 112 having a thermalconductivity equal to 1%. of the thermal conductivity of conductive line111.

The Wiedemann-Franz law, equation (1), is used to express the change intemperature ΔT in line 111 as a function of the metal resistivity,##EQU13##

The Hagen-Rubens relation, equation (2), is used to relate the change intemperature to the reflection, ##EQU14## where the Taylor seriesexpansion of the resistivity has been used, ##EQU15## Substitutingequation (15) into (16), gives the reflectance in terms of thederivative of the resistivity with respect to temperature. The followingterms in equation (16), ##EQU16## do not vary with the modulation of theheating laser. The third term, in equation (16) ##EQU17## varies withthe modulation, and can be measured using synchronous detection. Thisthird term is used to find a change in reflectance, ##EQU18## where thefrequency of the probe light in terms of its wavelength λ is ν=c/λ,where c is the speed of light.

From the Bloch-Grueneisen law, the temperature dependence of resistivityvaries as ##EQU19## where T.sub.θ is the Debye temperature (333 degreesKelvin for aluminum and 395 degrees Kelvin for copper) Relation (19)holds for T/T.sub.θ >0.25, and is generally valid at or above roomtemperature for the metals of interest in fabrication of wafers.

Taking the derivative of equation (19) and substituting into equation(18) gives the relation between the reflection and the resistance perunit length, ρ_(e) /wh_(m), ##EQU20##

Equation (20) is the governing equation of operation for act 206 ofmethod 200 described above. The measurements indicative of resistanceare carried out as follows: the amplitude of the reflected portion ofprobe beam 102 at the modulation frequency is measured as a voltagelevel and is converted using a calibration constant into reflectance(apparatus 13 is calibrated using samples having known reflectance toobtain a scaling factor that when multiplied with a measured voltagelevel yields the reflectance). The reflectance is then plotted (see line601 in FIG. 6) as a function of the power of heating beam 101. The slope(ΔR/ΔP) of the resulting line 601 provides a value of the followingpartial product in equation (20) that includes everything but the powerP_(L) of heating beam 101: ##EQU21## The above partial product containsall known parameters except for resistance per unit length, ρ_(e)/Wh_(m) at the Debye temperature T.sub.θ. Therefore, the resistance perunit length ρ_(e) /Wh_(m) is found by dividing the slope (ΔR/ΔP) (alsocalled "steady state ratio" and obtained as described above) with thefollowing constant: ##EQU22## In an example, the constant is 0.723 forline 601 in FIG. 6, assuming the conductive material is aluminum,dielectric layer underlying line 601 has a thickness of 1.0 μm, thewavelength of probe beam is 1.48 μm, and reflectance is 0.9. Therefore,probe beam's incident power is 1.1 mW, reflected power is 1.0 mW (in theabsence of heating beam) thereby resulting in reflectance R of 0.9 thatis used in the above formula to compute the constant 0.723. Thereafter,apparatus 13 divides a slope (ΔR/ΔP) computed as described above inreference to FIG. 6 with the constant to determine the resistance perunit length. Therefore, in the above-described example, apparatus 13divides the value 0.5 of (ΔR/ΔP) with the constant 0.723 to obtain avalue 0.361 for the resistance per unit length (in units of ohms/cm). Ifnecessary, resistivity ρ_(e) is found from the resistance per unitlength ρ_(e) /Wh_(m) using known values of line width W and linethickness h_(m). The just-described resistivity ρ_(e) is at the Debyetemperature, and can be used in equation (19) to obtain resistivity atany other temperature.

In equation (20) there is an extra factor of ##EQU23## in the numerator,but the thickness h_(m) is known (at least approximately), andvariations in thickness have a relatively small effect (e.g. less than1% because thickness is typically known to better than 2%), especiallyconsidering that equation (2) requires the square root of h_(m). As theresistance per unit length is ρ_(e) /Wh_(m), changes in the measuredvoltage level correspond to changes in the resistance per unit length.

The resistivity and slope with respect to temperature for a few metalsare:

    ______________________________________                                        Metal   Resistivity @ 20 C. (Ω-cm)                                                                ##STR1##                                            ______________________________________                                        Aluminum                                                                              2.23 × 10.sup.-6                                                                         1.2 × 10.sup.-8                                Copper  1.72 × 10.sup.-6                                                                         7.0 × 10.sup.-9                                Gold    2.44 × 10.sup.-6                                                                         9.1 × 10.sup.-9                                Nickel  7.80 × 10.sup.-6                                                                         3.4 × 10.sup.-8                                ______________________________________                                    

For an aluminum line with 0.25 μm width and 0.5 μm thickness,reflectance of 0.9, heating power of 5 mW at 830 nm, and probe power of1 mW at 1.48 μm, the reflected power is 2.7 microwatt.

As illustrated in FIG. 4B, when heated region 111R is adjacent to a via114 that connects line 111 to another conductive line 113 underneathdielectric layer 112, the heat generated by beam 101 branches into twocomponents, of which one component flows through via 114. Specifically,heat Q1 generated by beam 101 in line 111 in the negative λ directionbranches into (1) a first component heat Q2 in line 111 beyond thelocation of via 114, and (2) a second component heat Q3 that flowsthrough via 114. As Q1=Q2+Q3, any change in the magnitude of Q3 (e.g.due to a defect in via 114 caused by partially filled metal), affectsthe magnitude of heat Q1 diffusing out of heated region 111R.

Therefore, a measurement of the reflected power in region 111R at adistance V_(d) from defective via 114 is higher than a correspondingreflectance measurement at the same distance V_(d) from a normal(non-defective via) Note that distance V_(d) is smaller than the lengthL for the reflectance measurement to have a noticeable difference. Forexample, with reference to the change in temperature shown in FIG. 5,V_(d) can be chosen to be 5 microns, when length L is about 20 microns.Assuming the heat flow branches approximately equally between via 114and line 111 (e.g. Q2=Q3), a defective via may result in a 50% increasein the reflected power measurement (at distance Vd) when compared to ameasurement near a non-defective via.

Therefore, in one implementation, reflected power measurements areperformed adjacent to a number of vias, and each reflected powermeasurement that is noticeably greater (e.g. 25% greater) than theaverage measurement of a majority of the vias is flagged as indicating adefective via.

Such measurements could also be performed in a general manner in apredetermined set of regions (that are a fraction of the total number ofregions) related to vias (as described above), to detect a problem withthe process of forming vias that results in defective vias. If nodefective vias are found the wafer is processed further in the normalmanner (to form additional layers such as a dielectric layer followed bya metallization layer). If a defective via is found, the wafer isidentified as defective and placed in a cassette for further analysis(e.g. by probing, by sectioning or by scanning by electron microscope).

The measured signal level and the signal-to-noise ratio (SNR) iscalculated as follows. Equation (20) gives the power of the reflectedportion of probe beam 102 as a function of the power of heating beam101. If A (in units of amps/watt) is the conversion efficiency ofphotodetector 320 (FIG. 3), then the signal is generated as a current:

    I.sub.sig =AΔR(P.sub.L).sub.P.sub.P                  (21)

where reflectance ΔR(P_(L))is given in equation (20) and P_(P) is thepower of probe beam 102 (P_(L) is the power of heating beam 101 used togenerate the temperature distribution).

In one embodiment, a signal carried by current I_(sig) is converted to asignal indicated by a voltage level using a transimpedance amplifier 324(FIG. 3), and then amplified with a second amplifier 323, which is anamplifier providing a fixed voltage gain adjustable over the range of10× to 1000×. If the transimpedance gain is T_(g) (in units ofvolts/amp) and the amplifier gain is G, then the final signal has thevoltage level:

    V.sub.sig =GT.sub.g I.sub.sig =GT.sub.g AΔR(P.sub.L)P.sub.P(22)

Noise in the measured signal can arise from two components--noise inbeam 101 and shot noise in photodetector 320. Typically, shot noiseexceeds the noise in beam 101. The (RMS) of current due to shot noise is##EQU24## where BW is the noise bandwidth and q is the electron charge.For a probe beam 102 having power P_(p) =1 milliwatt, a noise bandwidthof 0.2 Hz, and a conversion efficiency of 0.5 Amp/watt, the noise poweris 11.3 picowatts and the noise current is 5.7 picoamps.

An equation for the signal-to-noise ratio is ##EQU25## For the values ofreflected power given above (2.7 μ watt for aluminum), the SNR is6.8×10⁴.

The predetermined frequency f at which heating beam 101 is modulated canbe made as low as necessary to provide a low noise bandwidth required ina particular case. However, as frequency f is reduced, lock-in amplifier322 (FIG. 3) must observe an increasing number of cycles of themodulation, thereby increasing the measurement time and decreasing thethroughput. A predetermined frequency of 100 Hz allows measurement in aperiod of 0.1 sec that is typically compatible with commercialthroughput requirements for processing production wafers, e.g. 2 minutesper wafer may be provided for the inspection of 13 sites on wafer 105(FIG. 1A). Under these conditions, the measurement period of 0.1 sec persite is negligible, and most of the throughput time may be used to loadand position wafer 105 in measurement apparatus 13.

In one implementation, two coaxial laser beams with wavelengths of 830and 1480 nanometers (for heating and probe beams respectively) arefocused onto a series of glass slides (not shown). Each of the glassslides have an aluminum coating of a different thickness in the range of400 to 1600 angstroms and was 1 inch wide and 3 inches long. A 0.9 NAobjective lens provides the 830 nm laser in a spot of diameterapproximately 1 μm. The beam from the 830 nm laser is modulated at 1KHz. The reflected portion of 1480 nm wavelength beam is sent through anarrow band filter to a germanium detector. The signal is then fed to alock-in amplifier and detected synchronously with the 830 nm lasermodulation.

The resistance between the two ends of each of the just-described glassslides is also measured (with an ohm meter). FIG. 7 illustrates, in agraph, a scatter plot comparing the measured resistance (X-axis) withthe measured reflection signal (Y-axis). A straight line 710 (alsocalled "correlation line") correlates the points on the graph, andillustrates the relationship between the actual resistance and themeasured reflectance. The linear correlation shown by line 710 indicatesthe theoretical basis for use of method 200 (FIG. 2) to obtain aresistance measure, as described above.

Numerous modifications and adaptations of the above-describedembodiments will become apparent to a person skilled in the art of usinglasers to measure semiconductor properties. For example, in analternative embodiment, instead of using a laser to generate heatingbeam 101 to change peak temperature Tp, another heat source (such as anelectron gun) is used to modulate the temperature T of a conductive linein a wafer. Use of electrons in beam 101 instead of photons allows thediameter of beam 101 to be made smaller than possible when usingphotons. However, use of electrons in beam 101 requires measurementapparatus 13 to include a vacuum chamber to contain the electron source.

Also, instead of measuring the steady-state ratio in a heated region(e.g. in region 111R), the measurement is performed in a regiondifferent from heated region 111R in another embodiment. Althoughmultiple measurements along conductive line 111 have been describedabove, such measurements need not be performed in a linear manner (e.g.along a straight line. Instead, method 200 (FIG. 2) can be used toperform measurements in an area, by focusing heating beam 101 in threedifferent regions successively (by performing act 202 for a firstregion, followed by performing act 210 for a second and third region),wherein the three regions together define a triangular area onconductive line 111, and measuring the power of the reflected portion ofthe probe beam at each of the three regions.

Note that the just-described method need not be performed on a singleconductive line 111, and instead each of the three regions could be onthree different conductive lines. Moreover, the three different regionscan be regions of a planar metallized area (not shown) of wafer 103 asdescribed below in reference to FIGS. 8A, 8B and 9. Also, instead ofonly three regions, a larger number (e.g. 100 regions) can be used togenerate a two dimensional graph (e.g. when the regions form a 10×10array) of the conductance of such a metallized area.

Furthermore, in another embodiment, a polarized beam of light is focusedon region 111R, and a polarization rotation upon reflection is measuredby interference, as described in the related U.S. patent application No.09/095,804, incorporated by reference above.

In another embodiment, the method is used to measure the properties ofthe underlying dielectric layer 112 (FIG. 1B). Specifically, the thermalprofile (that indicates temperature as a function of distance of a pointin layer 112 from line 111) is governed both by the characteristics(e.g. the thickness, width and thermal or electrical conductivity) ofline 111, and by the characteristics (e.g. the thickness and thermalconductivity) of dielectric layer 112.

Therefore, in one embodiment the characteristics (such as resistivity,thickness, and thermal conductivity) of a metal film (that is normallyetched to form line 111) are determined using a conventional method, andvariations in the thickness or thermal conductivity of the underlyingdielectric layer 112 are measured using the relationship in equation(20). In one implementation, characteristics of the metal film aredetermined by use of a four point probe. In another implementation, twowafers are prepared in an identical manner except for the followingdifferences: a first wafer includes, in dielectric layer 112, a knownmaterial, e.g. silicon dioxide, and a second wafer includes, indielectric layer 112, a material for which the properties are to bedetermined. The first wafer is used to measure the properties ofconductive line 111 (using reflectance measurements as described above),and thereafter the measured properties are used to determine thecharacteristics of dielectric layer 112.

In another embodiment, measurements are performed on an unpatternedlayer of conductive material, such as a layer formed by blanketdeposition over all regions of a wafer. In one implementation, theproperties of the conductive layer as a whole are substituted for thecorresponding variables. Moreover, for a conductive layer, the change inreflectance is determined from a solution of an area equation that issimilar to equation (20), but written in radial coordinates as follows:##EQU26## where Δ is the difference between the temperature at a radiusr and the ambient temperature, and the other variables are as definedearlier. The temperature profile is given by ##EQU27## where K₀ and K₁are modified Bessel functions, and the other variables are as definedearlier. Note that the temperature profile for a line, equation (15) wasa function of both the line thickness h_(m) and line width W. Inequation (26), the temperature profile for a conductive layer however,is only a function of the thickness h_(m) of the conductive layer.Therefore, a material property, specifically the resistance per unitthickness ρ_(e) /h_(m) (called the sheet resistance, or sheet rho) ofthe layer is determined as described above in reference to equations(1), (2), and (19).

A numerical model is used to obtain a curved line that relates thechange in reflectance (between the presence and absence of a heatingbeam) to the conductive layer's thickness (see line 801 in FIG. 8A) orbetween the change in reflectance and the sheet resistance (see line 851in FIG. 8B). This numerical model is analogous to the model for aconductive line, and uses the relations of equations (1), (2) and (19).FIG. 8A plots on the y axis the change in value of reflectancemeasurement multiplied by 10,000 and on the x axis the conductivelayer's thickness. A laser of 10 milliwatts at 1.48 μm wavelength isused to generate heating beam 101 (FIG. 1B). The four curves illustratedin FIG. 8A are for degradation in the resistivity for an aluminum filmof 0 (curve 801), 10% (curve 802), 50% (curve 803), and 100% (curve804). Therefore, in one example, resistance measurement apparatus 13measures reflected power from a conductive layer in the presence andabsence of heating beam 101, and determines the difference ΔR to be p4.2×10⁻⁴. Next, apparatus 13 interpolates, from line 801 (for nodegradation) the thickness h_(m) to be 0.4 μm. Therefore, if thethickness value of 0.4 μm falls within the specification (e.g. a rangeof 0.38 to 0.42 μm), then the substrate is processed further in thenormal manner, and otherwise the substrate is moved out of unit 10 (FIG.1A) for future analysis. Instead of line 801, any of other lines 802-804can be used depending on the resistance degradation required by aprocess. If the thickness h_(m) is known from another method, theresistance degradation can be determined.

FIG. 8B illustrates, in a graph, the sheet resistance, given by theresistivity divided by the thickness, on the x axis and the change inreflectance multiplied by 10,000 on the y axis. Line 851 is for analuminum film with resistivity degraded by 0% (in units of ohms/square).Therefore, in the above-described example, resistance measurementapparatus 13 uses the ΔR value of 4.2×10⁻⁴ to interpolate, from line851, the sheet resistivity to be 0.045. Apparatus 13 checks the measuredsheet resistivity with the specification for the resistivity in the samemanner as that described above in reference to FIG. 8A by comparisonwith a predetermined range of, e.g. 0.04 to 0.05.

Note that apparatus 13 need not compute a steady state ratio, andinstead can use a single reflectance measurement, or a differencebetween two reflectance measurements to determine the acceptability of aconductive layer (or a conductive line).

A transition from a measurement that is dependent on dimensions parallelto the plane of surface 105 (e.g. for a conductive line) to ameasurement that is dependent only on the thickness h_(m) of theconductive layer (e.g. when the conductive layer is yet to be patterned)occurs when the dimensions in the plane of surface 105 exceed thedistance at which the temperature rise becomes negligible. FIG. 9illustrates, in a graph, measurements taken at the center of squareregions, each region having a side of a different dimension from anotherregion. Each region is formed of aluminum and has a thickness of 0.2 μm.The regions have an underlying silicon dioxide insulator that is 1.0 μmthick. The y axis shows the value of reflectance measurement inmillivolts and the x axis shows the length of a side of a region. Forregions having a small length (e.g. less than 20 μm) the measured valueis a function of the dimensions in the plane of the surface. For regionshaving sides larger than about 20 μm, however, the measured value (alsocalled "signal") is independent of the dimensions in the plane of thesurface. Therefore, measurements on regions having sides greater than 20μm approximate the measurements for the entire layer.

Moreover, in one embodiment, the above-described measurements of thethermal conductivity of dielectric layer 112 are performed in a numberof successive regions of the wafer, e.g. in a linear scan across thewafer.

Therefore, numerous such modifications and adaptations of theabove-described embodiments are encompassed by the attached claims.

What is claimed is:
 1. A method for determining a property of a portionof a substrate, the method comprising:generating a first beam ofelectromagnetic radiation modulated at a predetermined frequency;focusing the first beam on a region on said substrate, the energy ofphotons in said first beam that are not reflected by said region beingconverted into heat, said predetermined frequency being sufficientlysmall to cause a majority of said heat to transfer by diffusion fromsaid region; measuring the power of a portion of a second beam ofelectromagnetic radiation, wherein the portion is reflected by saidregion, and is modulated in phase with modulation of said first beam. 2.The method of claim 1 wherein:said predetermined frequency is smallerthan a maximum frequency, said maximum frequency being inversely relatedto at least one of:length of a conductive line that includes said regionin said substrate; and a distance at which the temperature of saidconductive line is an order of magnitude smaller than the temperature insaid region.
 3. The method of claim 2 wherein:said conductive line has alength of approximately 100 microns; and said maximum frequency isapproximately 1000 Hz.
 4. The method of claim 2 furthercomprising:forming said conductive line in an integrated circuit die byusing at least one process parameter; and changing said processparameter depending on said power of said second beam.
 5. The method ofclaim 2 wherein the predetermined frequency is less than: ##EQU28##wherein: κ_(m) is thermal diffusivity of the metal; andL is length ofsaid conductive line.
 6. The method of claim 2 further comprising, afterthe generating, focusing and measuring:changing the power of said firstbeam; and measuring a change in power of said reflected portion of saidsecond beam in response to said changing.
 7. The method of claim 6further comprising:computing, in a programmed computer, a ratio of thedifference in power of said portion of said second beam to acorresponding difference in power of said first beam; and using saidprogrammed computer to compute the resistance per unit length of saidconductive line by dividing said ratio by a predetermined constant. 8.The method of claim 7 wherein said constant is determined from theformula: ##EQU29## wherein: c is speed of light in vacuumT is thicknessof said conductive line; λ is wavelength of said first beam; ε₀ is thedielectric constant of free space; q is the electron charge; k_(B) isthe Boltzmann's constant; R is absolute reflectance of said conductiveline; h_(m) is the thickness of the region; h_(i) is the thickness of aninsulating material underneath the region; K_(i) is the thermalconductivity of the insulating material; T₀ is the ambient temperature;and T.sub.θ is the Debye temperature.
 9. The method of claim 1wherein:said measuring includes using a lock-in amplifier tuned to saidpredetermined frequency.
 10. The method of claim 9 wherein saidmeasuring further includes:using a silicon wafer to filter out at leasta portion of said first beam reflected by said conductive line.
 11. Themethod of claim 10 wherein said measuring also includes:using a narrowband filter tuned to the wavelength of said second beam to filter out atleast another portion of said first beam reflected by said conductiveline.
 12. The method of claim 1 further comprising:comparing the powermeasured in said region with a predetermined limit.
 13. The method ofclaim 1 further comprising:focusing the first beam on a second regionadjacent to said region; and repeating said measuring.
 14. The method ofclaim 13 further comprising:changing a process parameter used infabricating said wafer if the power measured in said region is greaterthan the power measured in said second region by a predetermined limit.15. The method of claim 13 further comprising:focusing the first beam ona third region, wherein said region, said second region and said thirdregion define a triangular area on said conductive line; and repeatingsaid measuring.
 16. The method of claim 15 further comprising: changingthe power of said first beam; and repeating said measuring.
 17. Themethod of claim 1, wherein during said generating, said first beam has afirst power incident on said region at least ten times greater than asecond power of said second beam incident on said region.
 18. The methodof claim 1 wherein said power has a modulated component, the methodfurther comprising:dividing a parameter, related to the amplitude ofsaid modulated component by the value of said constant component toobtain a measure of the change in reflectance normalized by the absolutereflectance.
 19. The method of claim 1 further comprising, determiningthe value of at least one property of said region, and performing thefollowing acts after the generating, focusing and measuring:changing thepower of said first beam; measuring a change in power of said reflectedportion of said second beam in response to said changing; computing, ina programmed computer, a ratio of the difference in power of saidreflected portion of said second beam to a corresponding difference inpower of said first beam; and using said ratio and said value of saidproperty to compute the thermal conductivity of a dielectric layer lyingunderneath said region by dividing said ratio by a predeterminedconstant.
 20. The method of claim 19 wherein:said region is included ina conductive line.
 21. The method of claim 19 wherein said constant isdetermined from the formula: ##EQU30## where ε₀ is the dielectricconstant of free space, c is the speed of light,λ is the wavelength ofthe probe beam, q is the electron charge, k_(B) is Boltzmann's constant,R is the reflectivity of the region, h_(m) is the thickness of theregion, h_(i) is the thickness of an insulator lying under the region,T₀ is the ambient temperature, w is the line width, ρ_(e) (T.sub.θ) isthe resistivity at the Debye temperature.
 22. An apparatus forevaluating a wafer, said apparatus comprising:a first source of a firstbeam of photons having a first intensity modulated at a frequencysufficiently low to ensure transfer of a majority of heat from a regionilluminated by said first beam by diffusion; a second source of a secondbeam of photons having energy sufficiently lower than said energy ofsaid first beam to avoid generation of more than a negligible amount ofheat in said region when said second beam is incident on said region;and a photosensitive element located in a path of a portion of saidsecond beam, said portion being modulated at said frequency afterreflection by said region, said photosensitive element generating afirst signal indicative of an elevation in temperature of said regioncaused by incidence of said first beam.
 23. The apparatus of claim 22further comprising:a computer coupled to said photosensitive element andprogrammed to determine a ratio of the difference in power of saidportion of said second beam reflected by said region to a correspondingdifference in power of said first beam.
 24. The apparatus of claim 23wherein the computer is further programmed to compute the resistance perunit length of said region by dividing said ratio by a predeterminedconstant.
 25. The apparatus of claim 24, wherein the constant isdetermined from the following formula: ##EQU31## wherein: c is speed oflight in vacuum;T is thickness of said region; λ is wavelength of saidfirst beam; ε₀ is the dielectric constant of free space; q is theelectron charge; k_(B) is the Boltzmann's constant; R is absolutereflectance of said region; h_(m) is the thickness of region; h_(i) isthe thickness of an insulating film lying underneath the region; K_(i)is the thermal conductivity of the insulating film; T₀ is the ambienttemperature; and T.sub.θ is the Debye temperature.
 26. The apparatus ofclaim 23 wherein:the computer is further programmed to use said ratioand a known value of said property to compute the thermal conductivityof a dielectric layer lying underneath said region by dividing saidratio by a predetermined constant.
 27. The apparatus of claim 26wherein:the predetermined constant is the slope of a line obtained bycurve fitting a plurality of reflectance measurements on referencesubstrates.